A Weirdly Defined Function

Algebra Level pending

Let there be a function f ( x ) f(x) such that f ( x ) + 2 f ( a − x ) = 6 x f(x)+2f(a-x)=6x for all real x x and some constant a a . Then, f ( 10 ) f(10) can be written in the form a x − y ax-y . Find the value of x + y x+y .


The answer is 64.

Linus Setiabrata by Linus Setiabrata , 22, Indonesia

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1 solution

Rohit Sachdeva
Aug 31, 2014

first put x=10

f(10) + 2f(a-10) = 60........[1]

Then put (a-x) = 10, which means x = (a-10)

f(a-10) + 2f(10) = 6(a-10).......[2]

Eliminate f(a-10) from [1] and [2] to get

3f(10) = 12(a-10) - 60

f(10) = 4a - 60

Henca x=4 and y=60

x+y=64

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